Singular cohomology is a mathematical tool used in the field of algebraic topology to study the properties of topological spaces. It assigns a sequence of abelian groups or vector spaces to a space, capturing information about its shape and structure. This is done by considering continuous maps from standard geometric shapes, called simplices, into the space. The main idea is to analyze how these simplices can be combined and related to one another. By using cochains, which are functions that assign values to these simplices, singular cohomology provides a way to classify spaces based on their topological features, such as holes and voids.